1. Field of the Invention
The present invention relates to a numerical processing apparatus for deciding correspondence relation between output points in an output space of m dimensions and input points in an input space of n dimensions (m<n). Particularly, the invention relates to a color processing apparatus in a case where a CMYK color space and an L*a*b* color space are used as an input color space and an output color space, respectively on the assumption that a constraint condition is provided for input colors in the CMYK color space.
2. Description of the Related Art
Most printers receive color signals based on a color space such as RGB or L*a*b* and converts the color space into a CMYK color space having C (cyan), M (magenta), Y (yellow) and K (black) as elements, so that an image is formed by using color materials of C, M, Y and K. For various reasons caused by the image forming method and the properties of the color materials used in the printer, there is a possibility that the color of a formed image may be different from the color expressed by a received color signal. Therefore, color conversion is made at the time of formation of an image so that the color of the formed image and the color expressed by the received color signal coincide with each other as correctly as possible.
In order to obtain coincidence between the color of the formed image and the color expressed by the received color signal as described above, color conversion must be made while consideration is given to the characteristic of the printer. For this reason, a color signal in the CMYK color space, which generally serves as a color signal after color conversion is, for example, given as a color patch to form an image. The formed image is measured with a calorimeter to obtain a color signal, for example, in the L*a*b* color space. Then, a printer model is generated on the basis of a pair of the color signal in the CMYK color space and the color signal in the L*a*b* color space. A color signal in the L*a*b* color space is converted into a color signal in the CMYK color space in accordance with a model reverse to the printer model. As a result, the received color signal in the L*a*b* color space can be made substantially coincident with the measured value of the color of the formed image, so that faithful color reproduction can be achieved.
In the printer model generated in the aforementioned process, the CMYK color space is an input color space, and the L*a*b* color space is an output color space. The input-output relation in this printer model applies to the relation between the input (color) space and the output (color) space in the following description. When the color signal in the CMYK color space is obtained on the basis of the color signal in the L*a*b* color space in accordance with the reverse model, the value of the color signal in the CMYK color space cannot be decided uniquely because conversion of a three-dimensional space to a four-dimensional space is generally required. Therefore, the values of C, M and Y are predicted on the basis of the measured color signal in the L*a*b* color space and the value of K in the color patch.
In the printer, the total amount per pixel of the CMYK color materials used may be controlled in advance to ensure device performance. If the total amount of the predicted values of C, M and Y and the given value of K is larger than the threshold of total amount control, it is necessary to provide a process of controlling the total amount to be not larger than the threshold. If the value of K is not decided to satisfy the total amount control, the values of C, M and Y cannot be calculated.
A specific example will be described. Assume now that the allowable range of each of elements of C, M, Y and K is expressed as a range of from 0% to 100%. Assume that the total amount of C, M, Y and K is given by the expression:C+M+Y+K=315%when the threshold of total amount control is 300%, and the values of C, M and Y predicted on the basis of K=30% are C=100%, M=90% and Y=95% respectively. In this state, the total amount cannot satisfy the total amount control. Therefore, the value of K given together with the values of L*, a* and b* must be changed to thereby change the predicted values of C, M and Y to satisfy the total amount control.